The soil plate oscillator: Nonlinear mesoscopic elasticity of layers of glass beads in flexural vibration

Abstract

The soil plate oscillator (SPO) apparatus consists of two circular flanges sandwiching and clamping a thin circular elastic plate. In this presentation, uniform spherical glass beads—representing a nonlinear mesoscopic elastic material—are supported at the bottom by the plate and stiff cylindrical sidewalls of the upper flange. A small magnetic disk centered and fastened below the plate is driven by an AC coil placed below the magnet. Nonlinear tuning curves of the magnet’s acceleration are measured by driving the coil with a swept sinusoidal signal applied to a constant current amplifier. Experiments are first performed to measure the peak resonant frequency vs. mass loading as glass beads are added to make a level column above the plate. Experiments are repeated using 1,2,3,…,10 mm diameter beads to demonstrate how the frequency first decreases and then eventually increases for each bead diameter. Next, ten (separate) tuning curve experiments are performed using a fixed column of 350 grams of beads for ...